(a) Below is R code for simulating a discrete random variable Y. Determine the probability mass function (pmf) of Y.

Y.sim<-function(){

U<-runif(1)

Y<-1

while(U>1-1/(1+Y)){Y<-Y+1}

return(Y)

}

(b) Below is R code for simulating a discrete random variable Z. Show that Z has the same pmf as Y.

Z.sim<-function(){

U<-runif(1)

Z<-ceiling(1/U)-1

return(Z)

}

Will this function be faster or slower than Y.sim?